Japanese Artillery Square

This flat brass trapezoid has a rectangular shape cut out of one corner. Beginning at the left side of the rectangle and proceeding counter-clockwise, the corners have Japanese characters for the numbers 9, 4, 3, 5, and 7. The corners thus were used to draw regular polygons with 9, 4, 3, 5, and 7 sides. (For instance, the angle at the corner with the number 4 is 90°.) According to the accession record, the object was described as a ho kaku-gi (artillery or cannon square) and hoyo ki (artillery scale rule). A user would have made regular polygons in the course of designing fortifications and positioning artillery.
This square was displayed by the Japanese Empire Department of Education at the 1876 Centennial Exposition in Philadelphia. It then was held by the Museum of the U.S. Bureau of Education until it was transferred to the Smithsonian National Museum in 1910. For more information, see MA.261298 and MA.261313.
Currently not on view
date made
before 1876
place made
Physical Description
brass (overall material)
overall: 8.8 cm x 6.8 cm x .1 cm; 3 15/32 in x 2 11/16 in x 1/32 in
ID Number
catalog number
accession number
Credit Line
Transfer from Bureau of Education, Department of the Interior
See more items in
Medicine and Science: Mathematics
Science & Mathematics
Squares and Triangles
Data Source
National Museum of American History